BUS 219/MAT167 Online sections
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1. The average number of pounds of meat that a person consumes each year is 218.4 pounds. Let the standard deviation = 25 pounds and assume the distribution is approximately normally distributed. Find the probability that a randomly selected person (10 points)
a) Consumes less than 224 pounds per year
b) Consumes between 216 and 220 pounds per year
2. To help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 5% of students in the district based on a reading exam. The average score on that exam is 122.6 and the standard deviation is 18. Find the cutoff score needed to make a student eligible for the special reading program. (5 points)
3. Assume that the mean systolic blood pressure of normal adults is 122 milliliters of mercury with a standard deviation of 5.6 milliliters. Assuming a normal distribution, what is the probability that (11 points)
a) An individual teacher will have a pressure between 120 and 121.8 milliliters?
b) That a sample of 30 adults will have a pressure between 120 and 121.8 milliliters?
c) Explain the difference in the answers for parts a and b.
4. Women make up 24% of the science and engineering workforce. In a random sample of 400 science and engineering employees , what is the probability that (10 points)
a) More than 120 are women?
b) between 70 and 95 are women?
5. A researcher wishes to estimate the average amount of money that a person spends on lottery tickets per month. A sample of 50 people who play the lottery found a mean of $19 with a standard deviation of 6.8. Find the 95% confidence interval of the population mean. (5 points)
6. A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large pizza. How large a sample is needed is she wants to be accurate to within $0.15 given that a previous study found a standard deviation of $0.26? (5 points)
7. A recent study showed that 27 residents of Bowie had lived in their homes an average of 11.2 years. The standard deviation was 2. Find the 99% confidence interval of the true mean. (5 points)
8. A sample of 12 funeral homes in Ohio found these costs for cremation:
320 152 190 285 570 995
585 820 195 160 590 150
Find the 90% confidence interval for the population mean. (7 points)
9. In a recent study of 154 households, 54 had air conditioning. Find the 95% confidence interval of the true proportion who have air conditioning. (5 points)
10. Mr. Hoyack, and Dr. Jensen wish to estimate, within 0.05%, the true proportion of Cochise College students who study at least 3 hours each school night and they want to be 99% confident. (10 points)
a) How large a sample is necessary if a study two years ago showed that 65% of 450 students studied at least 3 hours each school night?
b) If no estimate of the sample proportion is available, how large should the sample be?
11. Find the 95% confidence interval for the standard deviation of the diameter of oranges if a sample of 47 oranges had a standard deviation of 0.18 inches. (5 points)
12. Jimmy Stewart, Tucson’s premier weather “guy”, claims that the average of the highest temperatures in the U.S. is 93 degrees. A random sample of 35 cities that have high temperatures has an average of 95.8 degrees with a standard deviation of 4.2. Test Jimmy’s claim at “alpha” = 0.05. (11 points; 3, 2, 3, 1, 2)
13. Nationwide, the average salary of college graduates is $39,000. A college placement officer feels that the average is higher for graduates at her college. She surveys 31 graduates and finds an average of $40,500 with a standard deviation of $4150. Can her claim be supported at “alpha” = 0.05? What about at “alpha” = 0.01? (11 points; 3, 2, 3, 1, 2)
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